Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions" and state how you arrived at that conclusion.
4x + 10y = 2
3x + 5y = 5
Since this is not my area of expertise, I searched Google under the key words "math elimination method" to get these possible sources:
http://answers.yahoo.com/question/index?qid=20070723210008AAa5Cfy
http://mathforum.org/library/drmath/view/52843.html
http://www.highpointsmath.com/sitemap/EliminationMethod.html
http://www.sci.wsu.edu/~kentler/Fall97_101/nojs/Chapter4/section1.html
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
I hope this helps. Thanks for asking.
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To solve the system of equations using the addition (elimination) method, we want to eliminate one of the variables by adding the two equations together. Let's start by multiplying the second equation by 2 to make the coefficients of the x terms the same:
Equation 1: 4x + 10y = 2
Equation 2: 6x + 10y = 10
Now, we can subtract Equation 1 from Equation 2:
(6x + 10y) - (4x + 10y) = 10 - 2
2x + 0y = 8
2x = 8
We are left with the equation 2x = 8. To solve for x, we divide both sides by 2:
2x/2 = 8/2
x = 4
Now that we have the value of x, we can substitute it back into either equation to solve for y. Let's use Equation 1:
4(4) + 10y = 2
16 + 10y = 2
10y = 2 - 16
10y = -14
Again, we divide both sides by 10 to solve for y:
10y/10 = -14/10
y = -1.4
Therefore, the solution to the system of equations is (x, y) = (4, -1.4).